Modern vehicles have braking systems which are operated autonomously or partly autonomously to decelerate the vehicle and to regulate the speed of the vehicle. Autonomously operated braking systems find application in vehicles driving autonomously, in which the driver has no possibility—or at most a very limited possibility—to influence the driving maneuvers executed by the vehicle. Braking systems that are operated partly autonomously can, in certain driving situations, initiate a braking maneuver without the driver having to become active for this purpose, even though he/she is sitting at the controls. Examples of such systems are adaptive cruise-control systems, in which by virtue of targeted braking interventions a certain spacing from the vehicle traveling ahead is not fallen short of. In the case of collision-avoidance systems a braking operation is initiated independently if an impact on an object—in particular with another vehicle—is predicted. Further applications of braking systems that are operated partly autonomously are traffic jam assistants, in which—up to a certain vehicle speed, particularly in a traffic jam—the driver must neither accelerate nor decelerate the vehicle. Moreover, in the case of parking assistants, which maneuver the vehicle independently into a parking space or into a garage, braking systems are actuated autonomously.
The vast majority of braking systems that are also employed in modern vehicles are operated hydraulically or pneumatically. Braking systems of such a type exhibit a relatively coarse dispersal of the pressure of the pressure medium, with the consequence that they can be operated only with a minimal braking torque which deviates more or less clearly from 0 Nm. Depending upon the braking system, the minimal braking torque amounts to between 30 Nm and 50 Nm. If a braking torque is required that lies below this braking torque, the braking system does not react. This results in the situation that a vehicle that is moving at a slow speed can be decelerated only relatively jerkily, since at least the minimal braking torque has to be used, even if a lower braking torque would suffice for the purpose of decelerating. In addition, the case may arise that the vehicle rolls for a certain time even though the control unit has initiated a braking operation, which from the point of view of safety is problematic.
Besides the losses of comfort, yet further disadvantages are associated with this: as already mentioned, the instantaneous speed of the vehicle plays a very important role for the braking operation and the required braking torque. The speed of the vehicle can be ascertained with an incremental encoder associated with one (or more) of the vehicle wheels, for instance. Such encoders produce a signal, or “tick,” for each angular increment of wheel rotation (change of angle of the wheel) being monitored. The speed signals or ticks are passed on to a control unit which, in turn, activates the braking system in a manner depending on the ascertained speed of the vehicle.
In many cases the control unit of the vehicle in question uses a so-called PI controller (proportional-integral controller), which is composed of a proportional term and an integrating term. PI controllers are part of a linear control concept wherein the above-described property of hydraulically or pneumatically operated braking systems, namely of reacting only as from a certain brake pressure, represents an instability which can only be managed with difficulty with PI controllers, despite the integrating term.
Since in the case of the PI controller it is a question of a stable controller, at low speeds it may occur that the incremental encoder produces no speed signal for a certain time, even though the vehicle is moving, and the PI controller no longer has a command variable and does not know whether or not the vehicle is moving.
If, for instance, an autonomously moving vehicle is to be driven into a garage or into a parking space, as a result of this the situation may occur that the vehicle comes to a halt short of (before reaching) the stipulated stopping position (target position), even though it still has to be moved at a low speed in order to reach the target position. In this case the control unit releases the brakes, and the vehicle is accelerated, in order subsequently to be decelerated again with the minimal braking torque already mentioned above. By this means, an undesirable sequence of acceleration processes and braking processes occurs. This sequence of acceleration processes and braking processes may be intensified if the vehicle is accelerated by external influences such as a gust of wind or by reason of the gradient of the parking space.
A further point is that during the transition from relatively high to low vehicle speeds, which in the following are to be designated as creeping speed, the friction, in particular between the wheels of the vehicle and the ground, passes over from a dynamic behavior into a static behavior, as a result of which the dynamics of the vehicle change, further aggravating the regulation of the braking processes.
U.S. Pat. No. 7,035,727 B2 presents a method for regulating the speed of a vehicle when the vehicle is moving at the creeping speed. EP 0 927 671 B1 presents a method for braking a wheel of a vehicle. Further disclosures for regulating the speed of a vehicle and also for braking a vehicle are to be found in JP 2004 032 826 A, JP 2000 278 815 A, US 2008/0115993 A1, U.S. Pat. No. 6,385,527 B1 and WO 2015/176876 A1